Introduction

A “joint model” describes two or more types of observation that typically depend on each other. A PKPD model is a “joint model” because the PD depends on the PK. Here we demonstrate how several observations can be modeled simultaneously. We also discuss the special case of sequential PK and PD modelling, using either the population PK parameters or the individual PK parameters as an input for the PD model.

Fitting first a PK model to the PK data

The column DV of the data file contains both the PK and the PD measurements: in Monolix this column is tagged as an OBSERVATION column. The column DVID is a flag defining the type of observation: DVID=1 for PK data and DVID=2 for PD data: the keyword OBSERVATION ID is then used for this column.

We will use the model oral1_1cpt_TlagkaVCl from the Monolix PK library

Only the predicted concentration Cc is defined as an output of this model. Then, this prediction will be automatically associated to the outcome of type 1 (DVID=1) while the other observations (DVID=2) will be ignored.Remark: any other ordered values could be used for OBSERVATION ID column: the smallest one will always be associated to the first prediction defined in the model.

Sequential PKPD modelling

In the sequential approach, a PK model is developed and parameters estimated in the first step. For a given PD model, different strategies are then possible for the second step, i.e., for estimating the population PD parameters:

Using estimated population PK parameters

Population PK parameters are set to their estimated values but individual PK parameters are not assumed to be known and sampled from their conditional distributions at each SAEM iteration. In Monolix, this simply means changing the status of the population PK parameter values so that they are no longer used as initial estimates for SAEM but considered fixed as on the figure below.

To fix parameters, click on the green option button (framed in green) and choose the Fixed method as on the figure below

The joint PKPD model defined in turnover1_model.txt is again used with this project.

Using estimated individual PK parameters

Individual PK parameters are set to their estimated values and used as constants in the PKPD model for the fitting the PD data. In this example, individual PK parameters were estimated as the modes of the conditional distributions . An additional column IGNORED OBSERVATION is necessary in the datafile in order to ignore the PK data. For that, we MDV=1 for the line where YTYPE=1 (PK data), and MDV=0 on the line where YTYPE=2 (PD data).

In addition, the estimated individual PK parameters (blue frame) are defined as regression variables, using the reserved keyword REGRESSOR. The covariates used for defining the distribution of the individual PK parameters are not mandatory as all the information is already in the individual parameters.
We use the same turnover model for the PD data. Here, the PK parameters are defined as regression variables (i.e. regressors).